A statistical mechanics framework for immiscible and incompressible two-phase flow in porous media. (January 2023) - Hansen, Alex; Flekkøy, Eirik Grude; Sinha, Santanu; Slotte, Per Arne
Abstract: We construct a statistical mechanics for immiscible and incompressible two-phase flow in porous media under local steady-state conditions based on the Jaynes maximum entropy principle. A cluster entropy is assigned to our lack of knowledge of, and control over, the fluid and flow configurations in the pore space. As a consequence, two new variables describing the flow emerge: The agiture, which describes the level of agitation of the two fluids, and the flow derivative, which is conjugate to the saturation. Agiture and flow derivative are the analogs of temperature and chemical potential in standard (thermal) statistical mechanics. The associated thermodynamics-like formalism reveals a number of hitherto unknown relations between the variables that describe the flow, including fluctuations. The formalism opens for new approaches to characterize porous media with respect to multi-phase flow for practical applications, replacing the simplistic relative permeability theory while still keeping the number of variables tractable. Highlights: We introduce a statistical mechanics framework for immiscible two-phase flow in porous media. The framework is built on defining an entropy associated with the fluid configurations at the hydrodynamic level. This leads to the definition of several new variables describing the flow at the Darcy scale. Among them are the agiture, a temperature-like variable, and the flow derivative playing the role of a chemical potential. A large number of relations emerge between the variables at the Darcy scale.